N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

The chemistry of copper is extremely rich because it can easily access Cu0, CuI, CuII, and CuIII oxidation states allowing it to act through one-electron or two-electron processes. As a result, both radical pathways and powerful two-electron bond forming pathways via organmetallic intermediates, similar to those of palladium, can occur. In addition, the different oxidation states of copper associate well with a large number of different functional groups via Lewis acid interactions or π-coordination. In total, these feature confer a remarkably broad range of activities allowing copper to catalyze the oxidation and oxidative union of many substrates.

Oxygen is a highly atom economical, environmentally benign, and abundant oxidant, which makes it ideal in many ways.1 The high activation energies in the reactions of oxygen require that catalysts be employed.2 In combination with molecular oxygen, the chemistry of copper catalysis increases exponentially since oxygen can act as either a sink for electrons (oxidase activity) and/or as a source of oxygen atoms that are incorporated into the product (oxygenase activity). The oxidation of copper with oxygen is a facile process allowing catalytic turnover in net oxidative processes and ready access to the higher CuIII oxidation state, which enables a range of powerful transformations including two-electron reductive elimination to CuI. Molecular oxygen is also not hampered by toxic byproducts, being either reduced to water, occasionally via H2O2 (oxidase activity) or incorporated into the target structure with high atom economy (oxygenase activity). Such oxidations using oxygen or air (21% oxygen) have been employed safely in numerous commodity chemical continuous and batch processes.3

However, batch reactors employing volatile hydrocarbon solvents require that oxygen concentrations be kept low in the head space (typically <5–11%) to avoid flammable mixtures, which can limit the oxygen concentration in the reaction mixture.4,5,6 A number of alternate approaches have been developed allowing oxidation chemistry to be used safely across a broader array of conditions. For example, use of carbon dioxide instead of nitrogen as a diluent leads to reduced flammability.5 Alternately, water can be added to moderate the flammability allowing even pure oxygen to be employed.6 New reactor designs also allow pure oxygen to be used instead of diluted oxygen by maintaining gas bubbles in the solvent, which greatly improves reaction rates and prevents the build up of higher concentrations of oxygen in the head space.4a,7 Supercritical carbon dioxide has been found to be advantageous as a solvent due its chemical inertness towards oxidizing agents and its complete miscibility with oxygen or air over a wide range of temperatures.8 An number of flow technologies9 including flow reactors,10 capillary flow reactors,11 microchannel/microstructure structure reactors,12 and membrane reactors13 limit the amount of or afford separation of hydrocarbon/oxygen vapor phase thereby reducing the potential for explosions.

Enzymatic oxidizing systems based upon copper that exploit the many advantages and unique aspects of copper as a catalyst and oxygen as an oxidant as described in the preceding paragraphs are well known. They represent a powerful set of catalysts able to direct beautiful redox chemistry in a highly site-selective and stereoselective manner on simple as well as highly functionalized molecules. This ability has inspired organic chemists to discover small molecule catalysts that can emulate such processes. In addition, copper has been recognized as a powerful catalyst in several industrial processes (e.g. phenol polymerization, Glaser-Hay alkyne coupling) stimulating the study of the fundamental reaction steps and the organometallic copper intermediates. These studies have inspiried the development of nonenzymatic copper catalysts. For these reasons, the study of copper catalysis using molecular oxygen has undergone explosive growth, from 30 citations per year in the 1980s to over 300 citations per year in the 2000s.

A number of elegant reviews on the subject of catalytic copper oxidation chemistry have appeared. Most recently, reviews provide selected coverage of copper catalysts14 or a discussion of their use in the aerobic functionalization of C–H bonds.15 Other recent reviews cover copper and other metal catalysts with a range of oxidants, including oxygen, but several reaction types are not covered.16 Several other works provide a valuable overview of earlier efforts in the field.17 This review comprehensively covers copper catalyzed oxidation chemistry using oxygen as the oxidant up through 2011. Stoichiometric reactions with copper are discussed, as necessary, to put the development of the catalytic processes in context. Mixed metal systems utilizing copper, such as palladium catalyzed Wacker processes, are not included here. Decomposition reactions involving copper/oxygen and model systems of copper enzymes are not discussed exhaustively. To facilitate analysis of the reactions under discussion, the current mechanistic hypothesis is provided for each reaction. As our understanding of the basic chemical steps involving copper improve, it is expected that many of these mechanisms will evolve accordingly.

/pdf/aerobic-copper-catalyzed-organic-reactions-3ctljpvivz.pdf

Aerobic Copper-Catalyzed Organic Reactions

5. M. Green, J. Schwarz, and E. Witten, Superstring theory, Cambridge Univ. Press, 1987. 6. J. Isenberg, P. Yasskin, and P. Green, Non-self-dual gauge fields, Phys. Lett. 78B (1978), 462-464. 7. B. Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential Geometric Methods in Mathematicas Physics, Lecture Notes in Math., vol. 570, SpringerVerlag, Berlin and New York, 1977. 8. C. LeBrun, Thickenings and gauge fields, Class. Quantum Grav. 3 (1986), 1039-1059. 9. , Thickenings and conformai gravity, preprint, 1989. 10. C. LeBrun and M. Rothstein, Moduli of super Riemann surfaces, Commun. Math. Phys. 117(1988), 159-176. 11. Y. Manin, Critical dimensions of string theories and the dualizing sheaf on the moduli space of (super) curves, Funct. Anal. Appl. 20 (1987), 244-245. 12. R. Penrose and W. Rindler, Spinors and space-time, V.2, spinor and twistor methods in space-time geometry, Cambridge Univ. Press, 1986. 13. R. Ward, On self-dual gauge fields, Phys. Lett. 61A (1977), 81-82. 14. E. Witten, An interpretation of classical Yang-Mills theory, Phys. Lett. 77NB (1978), 394-398. 15. , Twistor-like transform in ten dimensions, Nucl. Phys. B266 (1986), 245-264. 16. , Physics and geometry, Proc. Internat. Congr. Math., Berkeley, 1986, pp. 267302, Amer. Math. Soc, Providence, R.I., 1987.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics (Roger Temam)

In 1982, the Belgian Pilots' Guild raised the question of what effect exposure to radar radiation--for example, that encountered in passing a pilot launch's radar--might have on the human body. Recapitulating investigations of this question, this article states that in 25 years of experience with radar, there have been no known incidents of pilots being affected by radar waves. In the future, however, involvement by some pilots with Vessel Traffic Service shore-based radar could affect pilots somewhat differently from limited exposure to pilot launch radar. Pilots who find themselves in new working conditions close to an emitting source should exercise care all times.

About heat waves

Effect of a novel physical pretreatment process on the drying kinetics of seedless grapes

The rigid-rod model is capable of predicting several rheological features of rodlike polymers in the nematic phase. The model is formulated in terms of a nonlinear partial differential equation that describes the evolution of an orientational distribution function. The morphological properties and the rheological response of the sample can be determined once the distribution function is known. In this article the rigid-rod model is thoroughly analyzed with tools typical of bifurcation analysis for the case of shear flows. New flow regimes, both stationary and periodic, are found and illustrated. The detailed description of the model bifurcation structure allows some considerations about up to date closure approximations.

The rigid-rod model for nematic polymers: An analysis of the shear flow problem

A rheological model for rodlike polymers in the nematic liquid-crystalline phase is analyzed to characterize irregular dynamical response under pure shear flows. The model is studied with a continuation approach, and a period doubling scenario is detected. Time series generated via simulation are studied with nonlinear analysis tools to prove the existence of chaotic regimes.

/pdf/prediction-of-chaotic-dynamics-in-sheared-liquid-crystalline-5fda9tlhjn.pdf

Silvestro Crescitelli

Papers

Effect of a novel physical pretreatment process on the drying kinetics of seedless grapes

The rigid-rod model for nematic polymers: An analysis of the shear flow problem

Prediction of chaotic dynamics in sheared liquid crystalline polymers.

Mathematical modeling of eggplant drying: Shrinkage effect

Numerical model of ignition processes of polymeric materials including gas-phase absorption of radiation